Another intricacy in the formulation of (REF ) is the discrete indicator function in constraint (). This indicator function characterizes whether user \(u\)  is served by the \(b\) -th BS in cluster \(q\) , i.e., depending on whether the beamforming vector of the link between \(u\)  and \(q\)  is nonzero. Hence, the fronthaul capacity of BS \(b\)  is the summation of the rates of the users served (or cooperatively served) by BS \(b\) . To make this constraint tractable, we propose relaxing the indicator function in constraint () using a sparse beamforming approach, as in [1]} and [2]}.
First, we observe that the argument of \( \mathbb {1} \lbrace \cdot \rbrace \)  in () is a positive real number (i.e., \(||\mathbf {w}_{u,b,q}||_2^2 \in \mathbb {R}^+\) ), and so the indicator function reduces to the \(\ell _0\) -norm. Then, we adopt the weighted \(\ell _0\) -norm approximation to convexify the \(\ell _0\) -norm [1]}, [4]}.
